There was another "Who's right out of these two arseholes?" debate in the papers last week. I'm not talking about a hate cleric and the home secretary, or a terrorist and a general, or someone who wants to restrict freedom of speech and someone who wants to deny the Holocaust. No, in this case it was a shopper and a shop assistant in a Sainsbury's.

I'm not saying they're both arseholes through and through. I simply don't know – I don't have enough examples of their behaviour to form a conclusion. But I certainly don't have a single example of either of them behaving well.

This is what seems to have happened: 26-year-old property manager Jo Clarke was shopping. She's "Arsehole 1" – and all of the reports of the events that followed stem from her account. We have no version from the shop assistant who remains anonymous and whom, in order to show no bias in favour of either woman, I'm going to refer to as "Arsehole A". So we haven't heard Arsehole A's side of the story. Maybe in her account, she wouldn't seem like an arsehole. But we can't be sure. Because, I promise you, Arsehole 1 definitely seems like an arsehole in hers.

So A1 and her shopping are at the checkout, which is staffed by AA, and A1 is talking on her mobile phone to her brother. This is what A1 says happened next: "I was standing at the foot of the till waiting to bag my shopping up, yet the lady on the checkout was just staring at me, when I stopped my conversation and said: 'Is everything OK?' She said: 'I will not check your shopping out until you get off your mobile phone.' I ended my call swiftly and said: 'Apologies, I didn't realise that it was Sainsbury's policy that you are unable to use your phone at the checkout', and she said: 'Well you learn something new every day.'"

It's a curious exchange, as it appears to have taken place between two people who place a high value on politeness – other people's politeness – but don't believe that cause will be furthered by providing any themselves. AA obviously felt it was rude of A1 to talk on the phone when she should have been interacting with people who were physically present. But I don't think she questioned whether or not it was also rude to passively-aggressively freeze until A1 put the phone down. I wonder if, on sober reflection, she thinks the phrase "I will not check your shopping out until you get off your mobile phone" is exactly charm school material either. And I'd be surprised if she feels the level of courtesy in a conversation has ever been lifted by the sarcastic use of the expression "You learn something new every day". Clearly she was indulging in retaliatory rudeness. Which is just as rude as the rudeness she was retaliating about.

Not that A1 did all she could to defuse the situation created by her phone gaffe. Even as she reported it herself, her apology sounds contemptuous. The word "apologies" is not as apologetic as "sorry", and the sentence "I didn't realise that it was Sainsbury's policy that you are unable to use your phone at the checkout" is a declaration of war – one that she then honoured by going to the "customer services desk" on her way out, establishing that the company's policy does not in fact discourage till-side mobile phone use, and extracting an apology and £10 in vouchers (despite which boon she said, "I won't be shopping there again, I'll go to Waitrose in Dartford instead", where, sadly, they won't be valid).

Some time after that, A1 posed for press photographs in front of a Sainsbury's sign while talking theatrically into her phone – they took quite a few, some with and some without sunglasses. She was obviously determined to make something out of all this, which is another factor causing me to suspect she was hiding behind the door the day they were handing out niceness.

But Sainsbury's apology and two-figure payout weren't the end of it. Journalists and online commenters were quick to commend AA's timely and unfairly disparaged advocacy of better phone etiquette. "AA is right, not A1!" they cried. "A1 is the arsehole, not AA!" Even Nick Clegg weighed in on his radio show, in support of AA, saying: "I have a sneaking sympathy for her", and also cheekily sharing with his listeners: "I strongly suspect I have spoken on the phone in a queue. I like to think I probably wouldn't do that at the front of a check-in queue." As Harry Hill says, the search for a new Peter Ustinov is over.

I find this media response odd and frustrating. I haven't got a sneaking sympathy for either of them. I think they both sound horrible and they deserve one another. The more time people like that spend arguing with each other, the less chance any of the rest of us will have to encounter them.

And I don't think all this is a good starting point for a debate about phone etiquette either. Of course it's maddening when people don't properly engage in conversations with colleagues or friends because they're phoning, texting or Googling. Of course that's rude. But I think a supermarket checkout is a grey area (it's all the plastic). The big retail chains have spent decades mechanising and dehumanising the shopping process. Thousands of small tills are unmanned nowadays and, just last week, Asda in York tried out a new high-speed conveyer-belt scanner that could put the likes of AA out of work for ever. The superstore business model has always been to take more and more staff out of the process. So it's not particularly surprising if customers no longer behave like they're popping into Arkwright's for six ounces of gobstoppers.

One effect of mobile and internet technology is to distract us from friends and family members with inane online chatter with strangers. But, in this case, A1 was distracted from talking to a stranger by a phone call to her brother. That doesn't strike me as the most corrosive manifestation of mobile technology.

This is just a story of two people pouring scorn on one another, each from their own perceived moral high ground. The only lesson in manners we can draw from it is that, if you're conversing with a stranger while feeling self-righteous, there's a higher than average probability that you're being rude.